Question 793744
If the line passes through the point (5, 2),
{{{a*5+b*2=4}}} or {{{5a+2b=4}}}
Solving for {{{y}}},
{{{ax+by=4}}}-->{{{by=-ax+4}}}-->{{{y=(-a/b)x+4/b}}}
we get the equation in the slope intercept form, where the slope is the coefficient of {{{x}}}, so
{{{-a/b=2/3}}}-->{{{-3a=2b}}}
 
Now we solve the system
{{{system(5a+2b=4,-3a=2b)}}}-->{{{5a-3a=4}}}-->{{{2a=4}}}-->{{{a=2}}}
and substituting into {{{-3a=2b}}} we get
{{{-3*2=2b}}}-->{{{b=-3}}}